Non-collinear magnetic configuration mediated exchange coupling at the interface of antiferromagnet and rare-earth nanolayers

Mn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{3}$$\end{document}3Ir/CoFe bilayer is a prototypical exchange-coupled antiferromagnet (AF)–ferromagnet (FM) system. Nevertheless, a strong exchange coupling between FM and rare-earth(RE) interfaces of Fe/Dy and Fe/Tb has been established earlier. Strong coupling at the FM–RE interface originates from the number of irreversible spins owing to the imbalance in the non-collinear configuration in RE. However, exchange coupling between AF–RE could not be established due to the minimal number of irreversible spins in AF and RE. A frustrated inter-domain magnetic interaction leads to the coexistence of spin-freezing-like ordering around the temperature range of helical spin modulation at the exchange-coupled interfaces of RE-based specimens. To overcome the lack of coupling between the AF–RE interface, we use a sandwich structure of AF–FM–RE layers (Mn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{3}$$\end{document}3Ir/CoFe/Dy) as we demonstrate establishing considerable exchange bias in the system. Changing the bias direction during field cooling introduces possible differences in non-collinear directions (helicities), which affects the number of irreversible spins and consequent exchange coupling differently for opposite directions. The non-collinear structures in RE are topologically stable; thus, their directions of orientation can be regarded as an additional degree of freedom, which can be manipulated in all-spin-based technology.

www.nature.com/scientificreports/ Earlier, evidence of superimposed helical magnetic configurations or 2 π domain walls within both materials of FM-RE or RE-RE were found [6][7][8][9] . Interestingly, magnetic investigations had also revealed an exchange bias coupling with superparamagnetic (SPM) or super spin-glass (SSG) like behavior, attributed to spin-frustrated interfaces 9 . However, exchange bias coupling between the non-collinear or collinear spin texture of Mn 3 Ir 10-13 and the helical spin structure of RE was rarely investigated. This is due to the fact that the exchange coupling between AF-RE is very weak for the two highly anisotropic materials. The lowest-order uniaxial AF and RE sublattice anisotropy constants are K RE ( K Dy ∼ 1.7 × 10 5 J/m 314 ) and K AF ( K Mn 3 Ir ∼ 6.2 × 10 5 J/m 315 ), respectively. Nevertheless, a strong coupling was established extensively between the AF-FM 6 and also between the FM-RE interfaces 7 . In REs like Tb or Dy, the presence of large orbital momentum leads to a strong spin-orbit coupling and larger magnetic anisotropy. The large difference in the spin-orbit coupling in AF and RE elements can have significant influences on the demagnetization processes as well. Aided by the RKKY interaction, the magnetic modulations usually propagate coherently over a long-range, even within the intervening nonmagnetic or magnetic layers.
The helical structures in rare-earth are essentially due to spatially modulated magnetic states in systems with competing exchange interactions. Thus, an FM layer sandwiched between AF and RE materials would be interesting to explore as we expect an indirect coupling between AF and RE layers via an FM layer. Inversion of the helicity with associated handedness or chirality can thereby be tailored for the RE coupled to the FM simply by flipping the field cooling direction for the underlying AF-FM system. Inverted helicity represents a π projection of the sublattice spin direction of motion, which undergoes a concomitant chirality ( ↔ ) reversal. A sketch in Fig. 1 shows the possible scenarios of helical-chirality inversion. The scenarios in the figure, however, are possible cases when we consider the helical phase of the RE. Since incoherent domain structures are expected, we need not consider the helical phase for the AF-based systems in interpreting their magnetic behavior. The manipulation and/or control of domain dynamics within AF-RE systems can facilitate the design and construction of functional chiral nanomaterials as an additional degree of freedom in all-spin-based spintronics. The inter-sublattice exchange between RE and transition-metal spins is antiferromagnetic 16 .
Here, we investigate the magnetic properties of AF-FM, AF-RE, and AF-FM-RE by interface engineering within heteroepitaxial and or polycrystalline bilayers. Exchange-biased coupling was evident for all three systems. It is negligibly weak for the AF-RE system around the temperature of the helical phase whereas it gains relatively higher values for the AF-FM-RE system around the same temperature range. We find a frustrated inter-domain magnetic interaction leading to the coexistence of spin-freezing like ordering around the temperature range of helical spin modulation at the exchange-coupled interfaces of AF-RE based specimen. Such spin-freezing phenomena cease to exist in the AF-FM-RE system, extending the SPM limit. Changing the bias direction during field cooling of the AF-coupled interface, across the intervening FM layer, we could introduce a difference in the non-collinear directions for opposite field cooling options and demonstrate its consequence on the bias field of the exchange-coupled RE layer.  X-ray diffraction. The X-ray diffraction (XRD) patterns in Fig. 2 show the structural characterisation for S1, S2, and S3. All samples depict a high degree of crystallographic orientation (epitaxy) for Mn 3 Ir and also for CoFe (in S1 and S3) while polycrystallinity is seen for Dy (in S2 and S3) and TaN  Ir are either split or superimposed, implying an in-plane strain in the films. The same reflections from CoFe (001 , 002 and 1 1 0, 2 2 0) in S1 and S3, on the other hand, are not distorted. No such reflections can be seen for TaN, implying a disordered lattice. Ring-like reflections, signifying polycrystallinity for TaN and Dy, are observed from S1 and S3, respectively. The hexagonal reflections for Dy in S2 are relatively distinct as compared to that in S3.
We perform detailed peak analysis from the FFT spots in estimating the lattice mismatches in all samples. For S1, we find a little lattice mismatch ( ≈ 5%) with MgO (001) (a = b = c = 4.217 Å), ensuring Mn 3 Ir (001) (a = b = c = 4.001 Å) to remain coupled to the substrate. This is sufficient to seed cube-on-cube growth, allowing a small epitaxial strain. The interface between Mn 3 Ir and CoFe lattices, on the other hand, did not see a sufficient mismatch ( ≈ 1%), ensuring an unstrained heteroepitaxial growth. For S2, the MgO/Mn 3 Ir interface show even smaller lattice mismatch ( ≈ 2%) than in S1 and that between Mn 3 Ir/Dy interface is not possible to determine due to a structural change in Dy. For S3, the MgO/Mn 3 Ir interface again show a little lattice mismatch ( ≈ 3%) while the Mn 3 Ir/CoFe interface show significantly small lattice mismatch ( ≈ − 0.1%). Similar to S2, here also, it is not possible to determine the mismatch between CoFe/Dy interface due to a structural change in Dy. Figure 3c shows the EDS spectrum for S1 and the corresponding EDS maps in Fig. 3d for elemental identification across the stack while the EDs maps for S2 and S3 are shown in Figs. 4c and 5c, respectively. The layers are readily identified with sharp interfaces from the EDS maps of the MgO substrate, Mn 3 Ir, CoFe, Dy, and TaN Figure 2. XRD for S1, S2, and S3. X-ray diffraction patterns of the epitaxial Mn 3 Ir (S1, S2 and S3) and CoFe (S1, S3) indicating the main structural peaks from the layers. The Dy peaks (S2 and S3) correspond to the various polycrystalline phases. Additionally, various peaks are seen from the capping layer (TaN) and substrate (MgO).       Magnetization measurements. Field cooled and zero-field cooled measurements. Characterization of the magnetic properties was done using the field-dependent magnetization (M) measurements as a function of temperature (T) using field cooled (FC) and zero-field cooled (ZFC) protocols. We applied different magnetic fields H a = 5 Oe (0.5 mT) to 500 Oe (50 mT) during measurements after cooling down to 2 K in presence of H a = 5 kOe/500 mT (FC) and 50 kOe/5000 mT (FC). The same protocol was used when the samples were cooled down to 2 K in the presence of no magnetic field (ZFC).
Samples S1 and S2. The magnetization (M(T)) curves are shown in Fig. 8 for S1 and in Fig. 9a,b for S2 at various applied fields. The ZFC curves for S1 in Fig. 8 do not show any peak while the FC curves shift to higher temperatures with an increase in field, typical for a ferromagnetic film. One may note that the antiferromagnet ( (d) Dy www.nature.com/scientificreports/ Ir) usually having a multi-domain structure would influence FC and ZFC curves differently due to the AF-FM coupling with the ferromagnet on top (CoFe). However, S2 (Fig. 9a,b) show broad ZFC maxima, which can be referred to as the blocking or freezing temperature ( T F ). The appearance of a peak in the ZFC curve within a range of 70-180 K suggests that it could have an origin owed to the assembly of magnetic spin-clusters, which can pass from a blocked or frozen state (SSG) to an SPM regime with an increase in temperature. One may note that a helical structure of Dy is expected to appear within a similar temperature range (87-179 K), at least in bulk. The plot of T F as a function of field H a  www.nature.com/scientificreports/ is shown in Fig. 9c for S2. We find T F to decrease with the field, which suggests that the frozen state is gradually suppressed by the field. With an increase in the magnetic field, as the crystal-field anisotropy starts to decrease, the thermal energy required to cross the height of energy barriers between the two easy axis orientations also decreases. A gradual convergence of the ZFC and FC curves with increasing field, indicates the attainment of a similar type of magnetic configuration near equilibrium for both samples.
The irreversibility temperature T irr , which usually indicates the divergence temperature for FC and ZFC curves, could be seen for S2 to shift to lower temperatures with increasing H a . The shift can follow the Almeida-Thouless (AT) line indicating an SSG-like behavior 18,19 . The expression for AT line is given by where T irr (0) is the zero-field freezing temperature and J is the width of the distribution of exchange interactions. The plot of H a 2/3 as a function of T irr is shown in Fig. 9d. The curve cannot be fitted to the AT line, which separates a nonergodic (SSG) phase from an ergodic (SPM) one, except for within a limited temperature range (150-165 K) as the fitted (blue dashed) line cuts the x axis at T irr (0) ≈ 165 K. Thus, S2 shows a collective freezing behavior, which resembles spin-glass type but within a limited temperature where one expects a helical phase for Dy.
Sample S3. Figure 10 shows the M(T) curves for S3. The ZFC curves do not show any peak. However, at low temperatures they show negative values for H a ≥ 100 Oe. The negative values turn positive at a certain temperature, which decreases with increasing H a (inset of Fig. 10). Competing ferromagnetic and antiferromagnetic interactions around the energy barrier landscape lead to domains of frozen spins with opposite polarizations, which manifest themselves as coexisting bidomain states 20 .
Field hysteresis loops. In-plane magnetic field hysteresis loops were measured at different temperatures for S1 after field cooling in presence of + 5 kOe/− 5 kOe (500 mT/− 500 mT) for positive (negative) biasing and for S2 and S3 specimens at various temperatures after field cooling in presence of + 70 kOe/− 70 kOe (7000 mT/− 7000 mT) for negative (positive) biasing. The saturation field of S1 (S2, S3) is 2 kOe (50 kOe, 50 kOe). The remanent mag- /2 ) are defined for the two branches of the hysteresis loops. The interface exchange field during the hysteresis cycle comprises of reversible ( n r ) and irreversible ( n ir ) components of moments for positive ( n + = n r + n ir ) and negative field directions ( n − = n r − n ir ) of the respective decreasing and increasing branches of the hysteresis loop. The difference in remanent magnetization δm r = [m + r + m − r ]/2 , attributed to the uncompensated spins [(n + -n − )/2] in AF usually referred to as the vertical shift, is also defined. H eb is proportional to the number of uncompensated spins.
Samples S1 and S2. We have shown in Fig. 11a the hysteresis loops for S1 after field cooling in presence of + 5 kOe (500 mT) and for S2 in Fig. 12a-p after field cooling in presence of + 70 kOe (7000 mT), both for positive biasing. The variation of m r and monotonic decrease of H c and H eb with increasing T are plotted for S1 (Fig. 11b) and S2 (Fig. 12q). The magnetization per unit volume is ≈ 2.3 µ B /atom at 2 K for S1 while it is ≈ 7.0 µ B /atom at 2 K for S2. The bulk values of magnetization are 2.58 µ B /atom and around 2.3 µ B /atom for thin film in CoFe 21 . For Dy, they are 10.6 µ B /atom in bulk 22 and 7.1 µ B /atom for thin film 9 .
For S1, neither m r nor H c (Fig. 11b) go to zero although H eb is seen to be gradually decreasing and tending to zero. All these are typical for an exchange-coupled ferromagnetic system. Observations of vertical magnetization shift, stemming from the antiferromagnet, are sparse as merely a fraction of the total moments in the system are participating. The temperature where H eb → 0, signifies the blocking temperature of the exchange-coupled www.nature.com/scientificreports/ system. The hysteresis loops for S1 showing H −/+ eb at 2 K is shown in Fig. 11c for two sets of field cooling, positive and negative, respectively. The corresponding hysteresis loops and H eb values are expectedly mirrored.
However, for S2 (Fig. 12q), both m r as well as H c go to zero, which indicate relaxation and magnetic irreversibility for T < T F , the effects that are typical for supermagnetic blocked or frozen spin-clusters 23 . One may note that a monotic decrease can also be indicative of a weakness of magnetic interactions. The energy barrier against the anisotropy appropriate for SPM/SSG relaxation can be reduced by applying an external field, which effectively vanishes the magnetization at a certain field value. This field is the coercive field, which is given by for an ensemble of non-interacting clusters of spins where K u is the anisotropy constant and m s is the saturation magnetization 24 . Thus, a linear behavior to the H c versus T 1/2 plot (inset of Fig. 12q) following Eq. (2) along with when m r tends to zero with increasing T, indicates SPM/SSG type of spin-clusters whereas a non-linear behavior indicates SSG type of spin-clusters. Here, a linear fit to the data (black dashed line) indicates that it is in a supermagnetic state at least below T F (0) = 150 K. The linearity extends up to ≈ 25 K. The signatures of supermagnetism is largely extended within the temperature range where one expects helical spin configuration for Dy.
The H −/+ eb as a function temperature is shown in Fig. 12r for two sets of field cooling, positive and negative, rendering the respective negative and positive exchange bias fields of equal and opposite magnitudes i.e., their values are expectedly mirrored. However, the temperature range, where a helical spin configuration of Dy is expected (marked in cyan, ranging from 25-150 K), shows meagre exchange bias fields (ranging from H eb = 1 ± 1 Oe to 10 ± 1 Oe), varying arbitrarily down the temperature. One may note that the helical configuration in Dy thin films, interfaced with another magnetic layer, can manifest itself within an extended or shifted temperature range than in bulk 7 . Note that the H eb values, within this temperature range, do not maintain their mirrored values as expected on account of their respective positive and negative biasing protocols. Interestingly, much higher H eb values, reaching up to − 115 ± 12 Oe/+ 117 ± 12 Oe (respectively for positive/negative biasing), can be seen at temperatures below 20 K where the Dy layer is supposed to remain in an FM state instead of a helical one. This shows that AF-RE exchange coupling is very weak in the helical phase of an RE whereas it is considerably higher in its FM phase. www.nature.com/scientificreports/ The non-collinear magnetic structure was predicted to be responsible for the vertical shift δm r . It was shown to be more readily observable in non-collinear in Fe/MnO 2 than in collinear AF-coupled systems 25 . Earlier, polarized neutron reflectivity revealed direct evidence of helices in the form of planar 2 π-DWs within both layers of Fe and Dy 6,7 and also within both materials of RE-RE 9 . Thus, the δm r factor, in turn, can be regarded as a footprint of non-collinearity or exchange-coupled helices within a RE-based system. Plot of δm +/− r versus temperature (Fig. 12r) Fig. 13a-l. Here, we see similar shifts for the bottom half (top half) along the decreasing (increasing) branch of the loops below 170 K. We categorize the hysteresis loops in terms of the superimposition of two-loop shifts: The first one is called the primary loop, centered around 0.0 Oe along the x axis. The second one is called the secondary loop, which has its center shifted horizontally along the x axis, positive and negative. Such a superposition of two loops (primary and secondary) has been reported earlier for Fe/Tb 10 and also in Fe/ Dy 7 and was named "double hysteresis loop" (DHL). Oppositely biased subsystems with equal magnitudes of exchange bias acting on the DHLs are symmetric. Furthermore, we find a systematic variation of the H eb values corresponding to the shift of the primary loops as a function of temperature. Three representative double-loop characters of the hysteresis are shown in Fig. 14a-c at three different temperatures, namely 2 K, 100 K, and 170 K. We also show the effect of two sets of field cooling, positive and negative, rendering the respective negative and positive exchange bias shifts of the loops in Fig. 14d-f.
The m r , H c and H eb values versus temperature are plotted in Fig. 15a subjected to positive and negative biasing, respectively for S3. For both field cooling protocols, the m r values never go to zero, even though the H c values tend to go to zero. The non-vanishing m r values is due to the presence of the CoFe layer. Both these www.nature.com/scientificreports/ factors indicate that there is no conventional supermagnetic type of spin freezing (SSG type) or blocking (SPM type) in S3, which is in contrast to what was observed in S2 (Fig. 12q). This is also in accordance with the lack of any ZFC peak for S3 (Fig. 10). However, the inset of Fig. 15a show a linear behavior for the H c versus T 1/2 plot following eq n 2. A linear fit to the data (black dashed line) indicates a supermagnetic-type of state at least below T F (0) = 120 K extending up to ≈ 25 K. We believe that the supermagnetism in S3, which is again owed to the helical spin configuration for Dy within the temperature range, is overshadowed by the presence of the FM layer.
In Fig. 15b we show the H −/+ eb and δm +/− r values as a function temperature for the two sets of field cooling, positive and negative. Higher H eb values, reaching up to 195 ± 20 Oe for negative/positive biasing is observed below 20 K where Dy turns FM. We find a small positive exchange bias for positive field cooling around 250 K and 300 K, which can be due to the fact that an antiferromagnetic interface monolayer reconstructs into a sufficiently rigid canted moments configuration 27 or an AF domain wall is created within 28 , as the RE layer becomes paramagnetic.
Most interestingly, we see four important features for S3: (i) Considerable exchange bias fields at temperatures (25-170 K) even where we expect the Dy helical structure to come into play. (ii) The H eb values are seen to oscillate as a function of temperature till they are damped down at a certain temperature ( ≈ 250 K). In a non-collinear structure, e.g. Dy, the pinned spins arise from the small imbalance in the number of spins in each magnetic sublattice due to the naturally occurring atomic disorder 26 . These pinned (uncompensated) spins are strongly coupled to the anisotropic bulk-like Dy helix, which explains their stability and thereby causes the H eb shift. These spins are also accompanied by a reversible component which explains the increase in H c .  Fig. 16. For S2, m r ≃ 0 and H eb has negligible contributions. For S3, however, both m r show and H eb are significantly higher than S2 and both show a change in sign around 60 K. These higher values here, indicate a change in the spin configuration due to a change in the spin helicity imposed by the cooling protocols. One may note that we do not expect a change in the spin helicity in S2, since there is hardly any AF-RE coupling (nor in S1, as there is no RE) but is definitely expected in S3 (due to strong AF-FM-RE coupling) as depicted in the sketch of Fig. 1 for the two different biasing directions.
We believe the results obtained here reflect the complexity of the magnetic structures formed by the couplings of unconventional noncollinear spin structures in FM-RE with the conventional AF-FM-RE structures. Even though the non-overlapping biases indicate the fact that there exists a difference in the spin imbalance within the RE sublattice forming the helices for the two cooling conditions, more quantitative analyses based on the understanding of the exact magnetic structure would be desirable using vector magnetometric techniques like polarized neutron reflectivity. The current work remains at a rough qualitative description of the measured results with the consideration of the noncollinear magnetic structure within RE material.

Summary and conclusion
The microscopic origin of the exchange bias effect in the prototypical AF-FM system is a small number of irreversible moments in AF sublattice (Mn 3 Ir), which couples with a collinear FM (CoFe) 10 . Strong exchange bias coupling along with non-collinear spin configuration in the form of a helix has also been established in recent times for various FM-RE systems (viz., Fe-Tb, Fe-Dy) 6,7 or RE-RE systems (viz., Dy-Tb) 9 . Owing to non-collinear magnetic sublattice in the form of a helix within an RE, exchange bias within coupled FM-RE systems is caused by a small statistical imbalance in the number of irreversible moments in RE causing a net field at the interface that pins the FM (in FM-RE) or an RE in its FM phase (in RE-RE). Notably, such an imbalance in RE cannot www.nature.com/scientificreports/ couple to the uncompensated moments in AF, thereby causing no exchange bias at the interface of an AF-RE system (viz., Mn 3 Ir-Dy) 17 . We also find the coexistence of spin-freezing-like ordering around the temperature range of non-collinear or helical spin modulation, which is due to the frustrated inter-domain magnetic interaction at the Mn 3 Ir-Dy interface. We demonstrate here the means to overcome the absence of coupling in AF-RE by using intervening spins of FM (CoFe), which couples both, the uncompensated spins in AF (Mn 3 Ir) and the non-collinear magnetic configuration in RE (Dy) within an AF-FM-RE system (Mn 3 Ir-CoFe-Dy). The dependence of spin helicity or directions of non-collinearity can, in principle, be induced by equal but opposite field cooling protocols. The magnetization measurements presented here, however, are not sensitive to helicity.
The change in vertical shifts in the magnetization curves within the AF-FM-RE system is used to furthermore follow the variation of H eb values as a function of temperature. We demonstrate the effect of opposite field  www.nature.com/scientificreports/ cooling protocols on H eb consequentially from the small statistical variation in the number of irreversible spins participating, which are distinctly different for the positive and negative fields biasing. Nevertheless in spite of the presence of the FM layer, a spin-freezing-like ordering remains coexistent for the RE layer. The enhanced understanding of controlling exchange bias by tailoring the arrangement of non-collinear magnetic spin sublattice will provide new avenues for optimizing exchange-biased systems at the nanoscale. Our findings provide not only new insights into the physical origin of exchange anisotropy at the interface of non-collinear spin structure in rare-earth and ferromagnet but also show the possibility of exploiting non-collinearity orientations as an added degree of freedom in the field of upcoming spintronic devices. The substrates were single crystalline MgO wafers of 5 ×5 mm 2 , which were cleaned in isopropyl alcohol before use and ultrasonically cleaned in acetone and ethanol, then clamped mechanically to a holder, and subsequently heated to 250 • C under vacuum for 30 min before deposition. The targets were disks of 2 inch diameter. The thicknesses of the targets were 0.25 inch for Dy (purity of 99.9%), 0.055 inch for Co 80 Fe 20 (purity of 99.95%), 0.125 inch for Mn 80 Ir 20 (purity of 99.95%) and 0.125 inch for TaN (purity of 99.5%). TaN and Mn 3 Ir were bonded to a copper backing plate. The targets were cleaned by pre-sputtering for 1-5 min in Ar atmosphere. The depositions were done at elevated substrate temperatures at 300 • C without post-annealing, to achieve a compromise between high quality crystal structure and a smooth surface for Mn 3 Ir and CoFe. The deposition temperatures for Dy and TaN were at room temperature (RT). The deposition rates were pre-calibrated and were about 0.03 nm/s for Mn 3 Ir, 0.07 nm/s for CoFe and 0.07 nm/s for Dy. The Ar pressures in the magnetron sputtering chamber were 4 ×10 −3 mbar for Mn 3 Ir, CoFe and Dy during deposition, while the base pressure was maintained at 1.6× 10 −8 mbar. Actual thicknesses were subsequently confirmed by measuring x-ray reflectivity, with fits to the data yielding individual layer thicknesses. The samples were grown with a high degree of crystallographic orientation (texture) for Mn 3 Ir and CoFe, while polycrystallinity was obtained for Dy and TaN with an in-plane easy axis for the individual layer thicknesses chosen as a standard procedure. X-ray diffraction. X-ray diffraction (XRD) measurements were performed on a Rigaku SmartLab (9 kW) diffractometer at the GTIIT lab.

Methods
Transmission electron microscopy. Specimen preparation for transmission electron microcopy (TEM) was carried out using a ThermoFisher Talos F200X at the Electron Microscopy center (GTIIT). Typical focus ion beam (FIB) Sample preparation for transmission electron microscope (TEM) was carried out using a Thermo Scientific Helios 5 DualBeam (SEM/FIB) system. Typical focused ion beam (FIB) procedures were applied to TEM sample preparation and low voltage (5 kV and 2 kV) was used for the final polishing to reduce ion-beamrelated sample amorphous damage. High-resolution TEM (HRTEM) observations were conducted in a Ther-moFisher Talos F200X TEM operated at 200 kV and images were recorded using Ceta 16M camera 200 kV and Velox Imaging software. Energy Dispersive X-ray Spectroscopy (EDS) experiments were conducted in a ThermoFisher Talos F200X TEM with Super-X EDS Detector. The data analysis for lattice mismatches was done using the line profiles along the spots generated by the Velox™ user interface from ThermoFisher Scientific™. The FFT simulation is generated using the SingleCrystal™ software.
Magnetometry. Conventional in-plane magnetizations were measured at various temperatures and fields using a superconducting quantum interference device (SQUID) magnetometer from Quantum Design (MPMS3) at Nanomagnetism and Advanced Scattering (Nam-AST) lab (Paul's Lab) within Guangdong Technion, Shantou.

Data availability
The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.